Statistics Seminar Series

Abstract: Gaussian random field models have become commonplace in the design and analysis of costly experiments. Thanks to convenient properties of associated conditional distributions, Gaussian field models not only allow approximating deterministic functions based on scarce evaluation results, but can also be used as a basis for evaluation strategies dedicated to optimization, inversion, uncertainty quantification, probability of failure estimation, etc.

In this talk, we will mainly focus on two recent contributions that concern the incorporation of so-called structural priors in Gaussian random field models. First, results on covariance-driven pathwise invariances of random fields will be presented. Simulation and prediction examples will illustrate how Gaussian random field models can incorporate a number of structural priors such as group invariances or harmonicity.

Second, these results will be extended and applied to global sensitivity analysis. In particular, we will present a functional ANOVA decomposition of covariance kernels, and discuss the interplay between sparsity properties of the covariance kernel and of corresponding Gaussian random field paths.